| With the rapid development of the big data era,traditional single-machine processing techniques and centralized optimization are no longer able to support new systems that require large-scale and highly complex multi-intelligent systems in various fields.Therefore,distributed optimization has emerged.Compared to centralized optimization,distributed optimization does not require a central coordinator to control the agents,but instead optimizes the global objective through mutual cooperation among agents.It is an efficient processing tool that is robust,low-cost,decentralized and highly scalable,playing an important role in artificial intelligence,electronic information technology and communication fields.Game theory is an important tool for social analysis,which studies and processes the interests of multiple participants.The goal of game theory research is to obtain an optimal strategy that allows each participant to achieve the best possible result.Game theory is applied in many fields,including economics,political science,biology,psychology,and more.With the development of distributed systems,game theory has been extended to become a hot research topic in distributed optimization.The general Nash equilibrium is an important concept in game theory,which refers to a balanced state where each participant in a game has adopted an optimal strategy and these strategies are coordinated with each other.Due to the large-scale network consuming a large amount of computing resources,distributed optimization should be introduced into generalized Nash equilibrium problem to solve it.However,the current distributed algorithms have the problem of low efficiency and accuracy in solving game problems and are not adaptable to environments with special conditions and complex constraints.Therefore,this thesis studies the use of distributed primal-dual operator-splitting algorithm to solve generalized Nash equilibrium,with the main research content as follows:(1)The distributed optimization problem of generalized Nash equilibrium with fulldecision information and partial-decision information is studied.The problem is transformed into the problem of finding the zeros of the sum of monotone operators by using variational inequalities In the game,the local decisions of players are coupled through shared affine constraints.Based on the criterion of whether accessing to all players’ actions,two edge-based distributed algorithms are proposed with full-decision information and partial-decision information,respectively.Based on the theory of positive definite matrix and related theorems,the parameter range is calculated.The convergence of the two algorithms is proven under locally constant step size through mathematical theory and related graph theory.Additionally,the effectiveness and superiority of the algorithms are validated through the Gurney model and cogeneration model.(2)This thesis studied the distributed optimization problem of finding generalized Nash equilibrium solutions for aggregative games.This study consider aggregative games with affine coupling constraints,where agents have partial information about the aggregate value and can only communicate with neighboring agents.The decision cost of each agent depends on some aggregate effect of the actions of all other agents,without requiring communication among multiple agents.Each agent only needs to exchange and maintain estimates of the aggregate and dual multipliers.The convergence of the algorithm is verified through the invariance of aggregate estimates and operator splitting theory using consistent subspaces.Finally,numerical simulation experiments are conducted based on a distributed charging strategy for intelligent charging stations.In summary,this thesis focuses on solving the distributed optimization problem of generalized Nash equilibrium under the background of multi-agent and on the basis of the existing research,the algorithm is designed by the proximal operator theory.It provides a new way to solve practical problems more efficiently and has certain theoretical value and practical application value. |
